# Properties

 Label 119952.fs Number of curves $2$ Conductor $119952$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fs1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.fs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fs1 119952ez1 $$[0, 0, 0, -25284, 1490335]$$ $$1302642688/54621$$ $$74954100722256$$ $$$$ $$331776$$ $$1.4271$$ $$\Gamma_0(N)$$-optimal
119952.fs2 119952ez2 $$[0, 0, 0, 12201, 5531218]$$ $$9148592/607257$$ $$-13333011799064832$$ $$$$ $$663552$$ $$1.7737$$

## Rank

sage: E.rank()

The elliptic curves in class 119952.fs have rank $$0$$.

## Complex multiplication

The elliptic curves in class 119952.fs do not have complex multiplication.

## Modular form 119952.2.a.fs

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{13} - q^{17} + 6q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 